Crossover frequencies in a multicomponent plasma

An attempt has been made to generalise a method developed earlier for the qualitative assessment of crossover frequencies (existence and behaviour) in multicomponent plasmas with one negative ion species to plasmas with any number of positive and negative ion species. It is shown that a great deal of qualitative information can be obtained regarding the crossover frequencies for any given plasma model without recourse to cumbersome numerical study. Possible applications of the study in the interpretation of frequency time spectrograms for the detection of negative ion whistlers and in the measurement of concentrations and masses of negative ions are noted.

An approximate mathematical procedure for the determination of characteristic parameters for a general case in three dimensional photoelasticity

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Measurement of the acoustical impedance of a black box at low frequencies using a shorter impedance tube

For the experimental evaluation of the acoustical impedance of a termination by the impedance-tube method at low frequencies, the length of the impedance tube is a problem. In the present paper, the method of exact analysis of standing waves developed by the authors for the stationary medium as well as for mean flow, has been extended for measurement of the acoustical impedance of a termination at low frequencies. The values of the tube attenuation factor and the wave number at the low frequency of interest are established from the experiment conducted, with the given impedance tube, at a higher frequency. Then, exciting the tube at the desired low frequency it is sufficient to measure sound pressure at three differenct locations (not necessarily the minima) in order to evaluate reflection coefficient and hence the impedance of the termination at that frequency.

Estimation of higher natural frequencies of polar orthotropic annular plates

A method based on an assumption that the radial bending moment is zero at a nodal circle is shown to yield accurate estimates of natural frequencies corresponding to higher modes of transversely vibrating polar orthotropic annular plates for various combinations of clamped, simply supported and free edge conditions. This method is found to be convenient for the determination of locations of nodal circles as well. Numerical investigations revealed that for small holes, nodal circles tend to move towards the outer edge with increasing number of nodal diameters. For large holes, it has been shown that the plate behaves like a long rectangular strip.

Experiments on the fine structure of turbulence

Investigations have been carried out of some aspects of the fine-scale structure of turbulence in grid flows, in boundary layers in a zero pressure gradient and in a boundary layer in a strong favourable pressure gradient leading to relaminarization. Using a narrow-band filter with suitable mid-band frequencies, the properties of the fine-scale structure (appearing as high frequency pulses in the filtered signal) were analysed using the variable discriminator level technique employed earlier by Rao, Narasimha & Badri Narayanan (1971). It was found that, irrespective of the type of flow, the characteristic pulse frequency (say Np) defined by Rao et al. was about 0·6 times the frequency of the zero crossings. It was also found that, over the small range of Reynolds numbers tested, the ratio of the width of the fine-scale regions to the Kolmogorov scale increased linearly with Reynolds number in grid turbulence as well as in flat-plate boundarylayer flow. Nearly lognormal distributions were exhibited by this ratio as well as by the interval between successive zero crossings. The values of Np and of the zero-crossing rate were found to be nearly constant across the boundary layer, except towards its outer edge and very near the wall. In the zero-pressure-gradient boundary-layer flow, very near the wall the high frequency pulses were found to occur mostly when the longitudinal velocity fluctuation u was positive (i.e. above the mean), whereas in the outer part of the boundary layer the pulses more often occurred when u was negative. During acceleration this correlation between the fine-scale motion and the sign of u was less marked.

A genetic algorithm with characteristic amplification through multiple geographically isolated populations and varied fitness landscapes

This paper proposes a new approach, wherein multiple populations are evolved on different landscapes. The problem statement is broken down, to describe discrete characteristics. Each landscape, described by its fitness landscape is used to optimize or amplify a certain characteristic or set of characteristics. Individuals from each of these populations are kept geographically isolated from each other Each population is evolved individually. After a predetermined number of evolutions, the system of populations is analysed against a normalized fitness function. Depending on this score and a predefined merging scheme, the populations are merged, one at a time, while continuing evolution. Merging continues until only one final population remains. This population is then evolved, following which the resulting population will contain the optimal solution. The final resulting population will contain individuals which have been optimized against all characteristics as desired by the problem statement. Each individual population is optimized for a local maxima. Thus when populations are merged, the effect is to produce a new population which is closer to the global maxima.

A genetic algorithm with characteristic amplification through multiple geographically isolated populations and varied fitness landscapes

This paper proposes a new approach, wherein multiple populations are evolved on different landscapes. The problem statement is broken down, to describe discrete characteristics. Each landscape, described by its fitness landscape is used to optimize or amplify a certain characteristic or set of characteristics. Individuals from each of these populations are kept geographically isolated from each other Each population is evolved individually. After a predetermined number of evolutions, the system of populations is analysed against a normalized fitness function. Depending on this score and a predefined merging scheme, the populations are merged, one at a time, while continuing evolution. Merging continues until only one final population remains. This population is then evolved, following which the resulting population will contain the optimal solution. The final resulting population will contain individuals which have been optimized against all characteristics as desired by the problem statement. Each individual population is optimized for a local maxima. Thus when populations are merged, the effect is to produce a new population which is closer to the global maxima.

Generalised regression estimation for domain class frequencies

This study examines the properties of Generalised Regression (GREG) estimators for domain class frequencies and proportions. The family of GREG estimators forms the class of design-based model-assisted estimators. All GREG estimators utilise auxiliary information via modelling. The classic GREG estimator with a linear fixed effects assisting model (GREG-lin) is one example. But when estimating class frequencies, the study variable is binary or polytomous. Therefore logistic-type assisting models (e.g. logistic or probit model) should be preferred over the linear one. However, other GREG estimators than GREG-lin are rarely used, and knowledge about their properties is limited. This study examines the properties of L-GREG estimators, which are GREG estimators with fixed-effects logistic-type models. Three research questions are addressed. First, I study whether and when L-GREG estimators are more accurate than GREG-lin. Theoretical results and Monte Carlo experiments which cover both equal and unequal probability sampling designs and a wide variety of model formulations show that in standard situations, the difference between L-GREG and GREG-lin is small. But in the case of a strong assisting model, two interesting situations arise: if the domain sample size is reasonably large, L-GREG is more accurate than GREG-lin, and if the domain sample size is very small, estimation of assisting model parameters may be inaccurate, resulting in bias for L-GREG. Second, I study variance estimation for the L-GREG estimators. The standard variance estimator (S) for all GREG estimators resembles the Sen-Yates-Grundy variance estimator, but it is a double sum of prediction errors, not of the observed values of the study variable. Monte Carlo experiments show that S underestimates the variance of L-GREG especially if the domain sample size is minor, or if the assisting model is strong. Third, since the standard variance estimator S often fails for the L-GREG estimators, I propose a new augmented variance estimator (A). The difference between S and the new estimator A is that the latter takes into account the difference between the sample fit model and the census fit model. In Monte Carlo experiments, the new estimator A outperformed the standard estimator S in terms of bias, root mean square error and coverage rate. Thus the new estimator provides a good alternative to the standard estimator.

Approximate methods for step function response of undamped non-linear spring mass systems with arbitrary hardening type spring characteristic

The possibility of applying two approximate methods for determining the salient features of response of undamped non-linear spring mass systems subjected to a step input, is examined. The results obtained on the basis of these approximate methods are compared with the exact results that are available for some particular types of spring characteristics. The extension of the approximate methods for non-linear systems with general polynomial restoring force characteristics is indicated.

Influence of the hydrogen bond on the N-H stretching frequencies in amino-acids

The spectra of glycine, its addition compounds and other amino-acids exhibit Raman lines in the region from 3250 cm.−1 to 2500 cm.−1 It has been shown that these lines cannot be assigned to N-H...O stretching vibrations, where the N atom has the covalency of three, but to N+-H...O stretching vibration where the N atom has the covalency of four. Using the data obtained with triglycine sulphate which has the largest number of N+-H...O bonds and whose H bond lengths are known, the correlation curve giving the relation between the N+-H...O stretching frequencies and the corresponding H bond lengths has been drawn. Using this correlation curve, the N+-H...O stretching frequencies appearing inα-glycine,γ-glycine, diglycine hydrochloride, diglycine hydrobromide,l-asparagine monohydrate anddl-alanine have been satisfactorily accounted for on the basis of the known hydrogen bond lengths in these substances.

Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates

This paper presents a unified exact analysis for the statics and dynamics of a class of thick laminates. A three-dimensional, linear, small deformation theory of elasticity solution is developed for the bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates. All the nine elastic constants of orthotropy are taken into account. The solution is formally exact and leads to simple infinite series for stresses and displacements in flexure, forced vibration and "beam-column" type problems and to closed form characteristic equations for free vibration and buckling problems. For free vibration of plates, the present analysis yields a triply infinite spectrum of frequencies instead of only one doubly infinite spectrum by thin plate theory or three doubly infinite spectra by Reissner-Mindlin type analyses. Some numerical results are presented for plates and laminates. Comparison of results from thin plate, Reissner and Mindlin analyses with these yield some important conclusions regarding the validity and effects of the assumptions made in the approximate theories.

Natural frequencies and modes of tapered skew plates

The vibration of simply supported skew plates having a linear variation in thickness in one direction is considered. Approximate analysis is made by using Lagrange's equations employing the double Fourier sine series in oblique co-ordinates to represent the deflected surface. Natural frequencies are obtained for rhombic plates for several ranges of thickness variation and skew angle. The nodal patterns plotted for a few typical configurations show interesting metamorphoses with variation in thickness and skew angle.

Crossover frequencies in plasmas with two species in the presence of the Coriolis force

Points out that, in the presence of the Coriolis force, a crossover frequency can exist in a plasma with only two species and comments on the results with respect to proton whistlers. (see abstr. A67926 of 1970).